To determine the amount of current required, we need to use Faraday's laws of electrolysis. The first law states that the mass of the substance deposited at an electrode is directly proportional to the quantity of electricity (or charge) that passes through the electrolyte.
Here, we have:
- The mass of the metal deposited, \( m \), is 0.02 kg.
- The electrochemical equivalent, \( z \), is 1.3 x 10-7 kg/C.
- The time during which the current is applied, \( t \), is 120 seconds.
According to Faraday's first law of electrolysis, the mass (\( m \)) can be calculated by the formula:
m = z \times I \times t
Where:
- m is the mass of the substance deposited (in kilograms).
- z is the electrochemical equivalent (in kg/Coulomb).
- I is the current (in amperes).
- t is the time (in seconds).
Rearranging the formula to solve for current \( I \):
I = \(\frac{m}{z \times t}\)
Substituting the given values into the formula:
I = \(\frac{0.02 \, \text{kg}}{1.3 \times 10^{-7} \, \text{kg/C} \times 120 \, \text{s}}\)
Calculating the denominator:
I = \(\frac{0.02}{1.56 \times 10^{-5}}\)
Solving for \( I \):
I = 1282.05 \, \text{A}
Thus, the appropriate amount of current required to deposit 0.02 kg of metal in 120 seconds is approximately 1.3 x 103 A.
